clausen 1.0.1

Rust implementation of Clausen functions.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75

use num::complex::Complex;
use num::Float;
use clausen::Cl;
mod common;


#[test]
fn test_values() {
    let eps = 1e-14;

    for n in [-10, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1000, 1001, 1000000].iter() {
        let values = common::read_data_file(&format!("Cl{}.txt", *n)).unwrap();

        for &(v, expected) in values.iter() {
            assert_eq_float!(v.cl(*n), expected, eps);
            assert_eq_float!(Complex::new(v, 0.0).cl(*n).re, expected, eps);
        }
    }
}


#[test]
fn test_complex_input() {
    let eps = 1e-14;

    assert_eq_complex!(Complex::new(1.0,  1.0).cl(-2), Complex::new( 0.50688457710655124,  0.50950616274374456), eps);
    assert_eq_complex!(Complex::new(1.0, -1.0).cl(-2), Complex::new( 0.50688457710655124, -0.50950616274374456), eps);
    assert_eq_complex!(Complex::new(1.0,  1.0).cl(-1), Complex::new(-0.08267495282794197,  0.49171277760817954), eps);
    assert_eq_complex!(Complex::new(1.0, -1.0).cl(-1), Complex::new(-0.08267495282794197, -0.49171277760817954), eps);
    assert_eq_complex!(Complex::new(1.0,  1.0).cl( 0), cot(Complex::new(0.5, 0.5))/2.0, eps);
    assert_eq_complex!(Complex::new(1.0, -1.0).cl( 0), coth(Complex::new(0.5, 0.5))*Complex::<f64>::i()/2.0, eps);
    assert_eq_complex!(Complex::new(0.0,  1.0).cl( 1), Complex::new(-0.0413248546129181, -1.5707963267948966), eps);
    assert_eq_complex!(Complex::new(0.0, -1.0).cl( 1), Complex::new(-0.0413248546129181, -1.5707963267948966), eps);
    assert_eq_complex!(Complex::new(0.0,  1.0).cl( 2), Complex::new( 1.5707963267948966,  0.9861797794993302), eps);
    assert_eq_complex!(Complex::new(0.0, -1.0).cl( 2), Complex::new(-1.5707963267948966, -0.9861797794993302), eps);
    assert_eq_complex!(Complex::new(1.0,  1.0).cl( 2), Complex::new( 1.4107754938116412, -0.1044778629291566), eps);
    assert_eq_complex!(Complex::new(1.0, -1.0).cl( 2), Complex::new( 1.4107754938116412,  0.1044778629291566), eps);
}


fn cot(z: Complex<f64>) -> Complex<f64> {
    1.0/z.tan()
}


fn coth(z: Complex<f64>) -> Complex<f64> {
    1.0/z.tanh()
}


#[test]
fn test_cl1() {
    assert_eq!(0.0.cl(1), std::f64::INFINITY);
}


#[test]
fn test_signed_zero() {
    let pz64 = 0.0_f64;
    let nz64 = -0.0_f64;

    for n in (-100..100).into_iter().step_by(2) {
        assert!(pz64.cl(n).is_sign_positive());
        assert!(nz64.cl(n).is_sign_negative());

        assert!(Complex::new(pz64, pz64).cl(n).re.is_sign_positive());
        assert!(Complex::new(pz64, pz64).cl(n).im.is_sign_positive());
        assert!(Complex::new(pz64, nz64).cl(n).re.is_sign_positive());
        assert!(Complex::new(pz64, nz64).cl(n).im.is_sign_negative());
        assert!(Complex::new(nz64, pz64).cl(n).re.is_sign_negative());
        assert!(Complex::new(nz64, pz64).cl(n).im.is_sign_positive());
        assert!(Complex::new(nz64, nz64).cl(n).re.is_sign_negative());
        assert!(Complex::new(nz64, nz64).cl(n).im.is_sign_negative());
    }
}